Molar from sedimentation equilibrium

Itou et al. [60] determined 0II/0C for isotropic solutions of poly(n-hexyl isocyanate) (PHIC) and dichloromethane (DCM) from sedimentation equilibrium data on narrow distribution PHIC samples. Figure 3 shows their results, where the ordinate Mw(0II/0c) represents the osmotic pressure increment on the molar concentration scale. 

SE g lTlOl- molar mass, obtained from sedimentation equilibrium... 

In the case of two-component solutions (e.g., a protein in water or dilute buffer), the formulae for the determination of molecular parameters are well established (e.g., [57S1, 73C1, 75V1, 92H1]). Partial specific volumes are required for the correction of sedimentation and diffusion coefficients to standard conditions, i.e. standardization of s and D values to pure water at 20 °C as solvent (5, O ) determination of molar masses from sedimentation and diffusion data (Ms,d) or from sedimentation equilibrium (Mse). 

Nonlinear regression analysis of the dependence of c2(r) upon (r), a transform of the radial distance i leads to evaluation of the reference thermodynamic activity, Mzzz(rf), and the osmotic second virial coefficient, Au/Mi, expressed on a weight basis (litre/g) rather than a molar basis (litre/mol). Furthermore, the values of Miy v/ and ps can be obtained by curve-fitting the sedimentation equilibrium distribution for low biopolymer concentrations (M fr) cf for all r) to the equations (5.36) and (5.37) in order to deduce the quantity [Mj( 1 - v/ps)] from the coefficient of the exponent (Winzor et al., 2001 Deszczynski et al., 2006). 

Equation 9.8.22 is needed for sedimentation equilibrium, a method of determining the molar mass of a macromolecule. A dilute solution of the macromoleeule is placed in the cell of an analytical ultracentrifuge, and the angular velocity is selected to produce a measurable solute concentration gradient at equilibrium. The solute concentration is measured optically as a function of r. The equation predicts that a plot of In (cb/c°) versus will be linear, with a slope equal to Mb (l — E p) jlRT. The partial specific volume is found from measurements of solution density as a function of solute mass fraction (page 234). By this means, the molar mass Mb of the macromolecule is evaluated. 

Fig. 6. Apparent isopotential specific volume, 2 (in cm g ), and buoyancy term, (1 - (j>2 Ps) of lactate dehydrogenase as a function of the molar concentration, C3, of phosphate buffer (K2HPO4/KH2PO4 buffer pH 7.0). From [83D1]. Specific volumes were obtained by digital densimetry (circles), sedimentation velocity (upward triangles), and sedimentation equilibrium (downward triangles). Filled and open symbols refer to 2 and (1 - 2 Ps)> respectively. Experimental details can be found in the reference. Reprinted from International Journal of Biological Macromolecules, Vol. 5, H. Durchschlag and R. Jaenicke, Partial specific volume changes of proteins ultracentrifugal and viscometric studies, pp. 143-148, 1983, with...

Equilibrium sedimentation studies are mostly used to investigate density differences in different macromolecules. The method has been used, for example, in research on the replication of N-labeled deoxyribonucleic acids. Theoretically, it is also suitable for distinguishing between polymer blends and true copolymers. In such studies, problems usually arise from the considerable back-diffusion and the wide molar mass distribution. The gradient curves are so strongly influenced by these two effects that there is considerable overlap in the curves for substances of differing densities. 

The Z-average molar mass (Z refers to the German word for centrifuge, i.e., Zentrifuge) is derived from equilibrium sedimentation. It is defined as... 

It is sometimes more convenient to measure the equilibrium distribution of molecules than the rate at which they sediment. At equilibrium, when the tendency of the solute to settle is balanced by the spreading effect of thermal motion, the molar mass can be obtained from the ratio of concentrations c lCi of the macromolecules at two different radii Ti and r respectively, in a centrifuge operating at angular frequency o ... 

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